World's Best Scientists 2026 revealed!
George Em Karniadakis

George Em Karniadakis

Award Badge
Mathematics
USA
2026
Award Badge
Mechanical and Aerospace Engineering
USA
2026

D-Index & Metrics

Mathematics

D-Index
139
Citations
103227
World Ranking
1
National Ranking
1

Mechanical and Aerospace Engineering

D-Index
133
Citations
99712
World Ranking
9
National Ranking
5

Physics

D-Index
135
Citations
99796
World Ranking
462
National Ranking
258

George Em Karniadakis publication distribution in Mathematics in 2026

The chart shows the distribution of publications by all Research.com ranked scientists in the field of Mathematics in 2026. The highlighted bar marks where George Em Karniadakis sits on this spectrum.

42–46 publications: 3 scientists 47–51 publications: 5 scientists 52–56 publications: 7 scientists 57–61 publications: 20 scientists 62–66 publications: 14 scientists 67–71 publications: 25 scientists 72–76 publications: 19 scientists 77–81 publications: 35 scientists 82–86 publications: 50 scientists 87–91 publications: 60 scientists 92–96 publications: 86 scientists 97–101 publications: 84 scientists 102–106 publications: 83 scientists 107–111 publications: 90 scientists 112–116 publications: 99 scientists 117–121 publications: 90 scientists 122–126 publications: 91 scientists 127–131 publications: 109 scientists 132–136 publications: 110 scientists 137–141 publications: 98 scientists 142–146 publications: 112 scientists 147–151 publications: 102 scientists 152–156 publications: 88 scientists 157–161 publications: 106 scientists 162–166 publications: 82 scientists 167–171 publications: 102 scientists 172–176 publications: 77 scientists 177–181 publications: 81 scientists 182–186 publications: 78 scientists 187–191 publications: 71 scientists 192–196 publications: 92 scientists 197–201 publications: 64 scientists 202–206 publications: 69 scientists 207–211 publications: 64 scientists 212–216 publications: 62 scientists 217–221 publications: 58 scientists 222–226 publications: 53 scientists 227–231 publications: 50 scientists 232–236 publications: 46 scientists 237–241 publications: 46 scientists 242–246 publications: 46 scientists 247–251 publications: 43 scientists 252–256 publications: 29 scientists 257–261 publications: 45 scientists 262–266 publications: 30 scientists 267–271 publications: 33 scientists 272–276 publications: 34 scientists 277–281 publications: 30 scientists 282–286 publications: 31 scientists 287–291 publications: 21 scientists 292–296 publications: 34 scientists 297–301 publications: 26 scientists 302–306 publications: 10 scientists 307–311 publications: 17 scientists 312–316 publications: 23 scientists 317–321 publications: 13 scientists 322–326 publications: 16 scientists 327–331 publications: 26 scientists 332–336 publications: 13 scientists 337–341 publications: 13 scientists 342–346 publications: 16 scientists 347–351 publications: 17 scientists 352–356 publications: 12 scientists 357–361 publications: 18 scientists 362–366 publications: 18 scientists 367–371 publications: 9 scientists 372–376 publications: 11 scientists 377–381 publications: 8 scientists 382–386 publications: 8 scientists 387–391 publications: 9 scientists 392–396 publications: 9 scientists 397–401 publications: 8 scientists 402–406 publications: 11 scientists 407–411 publications: 6 scientists 412–416 publications: 6 scientists 417–421 publications: 9 scientists 422–426 publications: 8 scientists 427–431 publications: 5 scientists 432–436 publications: 8 scientists 437–441 publications: 8 scientists 442–446 publications: 4 scientists 447–451 publications: 4 scientists 452–456 publications: 4 scientists 457–461 publications: 2 scientists 462–466 publications: 2 scientists 467–471 publications: 4 scientists 472–476 publications: 3 scientists 477–481 publications: 3 scientists 482–486 publications: 6 scientists 487–491 publications: 3 scientists 492–496 publications: 5 scientists 497–501 publications: 5 scientists 502–506 publications: 1 scientists 507–511 publications: 6 scientists 512–516 publications: 4 scientists 517–521 publications: 1 scientists 522–526 publications: 3 scientists 527–531 publications: 1 scientists 532–536 publications: 4 scientists 537+ publications: 100 scientists
42 publications 537+

This scientist: 760 publications — 99th percentile

99% of scientists in this discipline score the same or lower.

The last bar groups every scientist with 537 publications or more.

George Em Karniadakis D-index placement in Mathematics in 2026

The chart shows the D-index (discipline H-index) distribution of Mathematics scientists ranked by Research.com in 2026. The highlighted bar marks where George Em Karniadakis sits on this spectrum.

30 D-Index: 174 scientists 31 D-Index: 151 scientists 32 D-Index: 174 scientists 33 D-Index: 117 scientists 34 D-Index: 136 scientists 35 D-Index: 127 scientists 36 D-Index: 145 scientists 37 D-Index: 153 scientists 38 D-Index: 150 scientists 39 D-Index: 150 scientists 40 D-Index: 137 scientists 41 D-Index: 136 scientists 42 D-Index: 93 scientists 43 D-Index: 108 scientists 44 D-Index: 115 scientists 45 D-Index: 112 scientists 46 D-Index: 103 scientists 47 D-Index: 75 scientists 48 D-Index: 59 scientists 49 D-Index: 67 scientists 50 D-Index: 60 scientists 51 D-Index: 57 scientists 52 D-Index: 59 scientists 53 D-Index: 62 scientists 54 D-Index: 60 scientists 55 D-Index: 50 scientists 56 D-Index: 42 scientists 57 D-Index: 54 scientists 58 D-Index: 50 scientists 59 D-Index: 42 scientists 60 D-Index: 41 scientists 61 D-Index: 35 scientists 62 D-Index: 40 scientists 63 D-Index: 21 scientists 64 D-Index: 31 scientists 65 D-Index: 27 scientists 66 D-Index: 29 scientists 67 D-Index: 19 scientists 68 D-Index: 25 scientists 69 D-Index: 17 scientists 70 D-Index: 18 scientists 71 D-Index: 12 scientists 72 D-Index: 14 scientists 73 D-Index: 13 scientists 74 D-Index: 18 scientists 75 D-Index: 9 scientists 76 D-Index: 11 scientists 77 D-Index: 10 scientists 78 D-Index: 9 scientists 79 D-Index: 16 scientists 80 D-Index: 12 scientists 81 D-Index: 10 scientists 82 D-Index: 5 scientists 83 D-Index: 5 scientists 84 D-Index: 13 scientists 85 D-Index: 6 scientists 86+ D-Index: 99 scientists
30 D-Index 86+

This scientist: 139 D-Index — 100th percentile

100% of scientists in this discipline score the same or lower.

The last bar groups every scientist with 86 D-Index or more.

Research.com Recognitions

  • 2026 - Research.com Mathematics in United States Leader Award
  • 2026 - Research.com Mechanical and Aerospace Engineering in United States Leader Award
  • 2025 - Research.com Mathematics in United States Leader Award
  • 2025 - Research.com Mechanical and Aerospace Engineering in United States Leader Award
  • 2018 - Fellow of the American Association for the Advancement of Science (AAAS)
  • 2013 - THE J. TINSLEY ODEN MEDAL For outstanding contributions to stochastic differential equations, in particular modelling uncertainty with polynomial chaos and development of spectral and hp element methods on unstructured meshes
  • 2011 - ACM Gordon Bell Prize For "A new computational paradigm in multiscale simulations: Application to brain-blood flow."
  • 2010 - SIAM Fellow For contributions to stochastic modeling, spectral elements, and fluid mechanics.
  • 2007 - THE THOMAS J.R. HUGHES MEDAL
  • 2004 - Fellow of American Physical Society (APS) Citation For his innovative developments and his insightful applications of the spectralelement method in computational fluid dynamics
  • 2002 - Fellow of the American Society of Mechanical Engineers

Overview

George Em Karniadakis is affiliated with Brown University in the United States. Their research work spans multiple fields of study, with a significant focus on engineering and physics and astronomy.

Their main subfields of study include statistical and nonlinear physics, artificial intelligence, computational mechanics, aerospace engineering, and materials chemistry. Their research topics cover model reduction and neural networks, neural networks and applications, fluid dynamics and turbulent flows, probabilistic and robust engineering design, nuclear engineering thermal-hydraulics, blood properties and coagulation, and Gaussian processes and Bayesian inference.

George Em Karniadakis has contributed to several research publications and academic venues. Frequent publication venues include:

  • arXiv (Cornell University)
  • Journal of Computational Physics
  • Computer Methods in Applied Mechanics and Engineering
  • SSRN Electronic Journal
  • SIAM Journal on Scientific Computing

Recent notable papers authored or co-authored by George Em Karniadakis are:

  • Physics-informed machine learning, 2021, Nature Reviews Physics
  • Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations, 2020, Science
  • Physics-informed neural networks (PINNs) for fluid mechanics: a review, 2021, Acta Mechanica Sinica
  • NSFnets (Navier-Stokes flow nets): Physics-informed neural networks for the incompressible Navier-Stokes equations, 2020, Journal of Computational Physics
  • Physics-Informed Neural Networks for Heat Transfer Problems, 2021, Journal of Heat Transfer

The scientist has co-authored extensively with collaborators including Khemraj Shukla, Somdatta Goswami, Zongren Zou, Xuhui Meng, and Ameya D. Jagtap.

In addition to journal publications, George Em Karniadakis has contributed to academic books, notably one published by Cambridge University Press titled Spectral and Spectral Element Methods for Fractional Ordinary and Partial Differential Equations in 2024.

Awards received by George Em Karniadakis include:

  • Fellow of the American Association for the Advancement of Science (AAAS), 2018
  • THE J. TINSLEY ODEN MEDAL, 2013, for contributions to stochastic differential equations and development of spectral and hp element methods on unstructured meshes
  • ACM Gordon Bell Prize, 2011, for work on multiscale brain-blood flow simulations
  • SIAM Fellow, 2010, for contributions to stochastic modeling, spectral elements, and fluid mechanics
  • THE THOMAS J.R. HUGHES MEDAL, 2007
  • Fellow of American Physical Society (APS), 2004, for developments in computational fluid dynamics via spectral-element methods
  • Fellow of the American Society of Mechanical Engineers, 2002

Best Publications

  • Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

    Maziar Raissi;Paris Perdikaris;George E. Karniadakis

  • The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations

    Dongbin Xiu;George Em Karniadakis

  • Physics-informed machine learning

    George Em Karniadakis;Ioannis G. Kevrekidis;Lu Lu;Paris Perdikaris

  • Spectral/hp Element Methods for Computational Fluid Dynamics

    George Karniadakis;Spencer J. Sherwin

  • Microflows and Nanoflows: Fundamentals and Simulation

    George E Karniadakis

  • DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators

    Lu Lu;Pengzhan Jin;George Em Karniadakis

  • The Development of Discontinuous Galerkin Methods

    Bernardo Cockburn;George E. Karniadakis;Chi-Wang Shu

  • Physics-informed neural networks (PINNs) for fluid mechanics: a review

    Unknown

  • High-order splitting methods for the incompressible Navier-Stokes equations

    George Em Karniadakis;Moshe Israeli;Steven A Orszag

  • Modeling uncertainty in flow simulations via generalized polynomial chaos

    Dongbin Xiu;George Em Karniadakis

  • Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations.

    Maziar Raissi;Maziar Raissi;Alireza Yazdani;George Em Karniadakis

  • DeepXDE: A deep learning library for solving differential equations

    Lu Lu;Xuhui Meng;Zhiping Mao;George Em Karniadakis

  • REPORT: A MODEL FOR FLOWS IN CHANNELS, PIPES, AND DUCTS AT MICRO AND NANO SCALES

    Ali Beskok;George Em Karniadakis

  • Spectral/hp Element Methods for CFD

    George Em Karniadakis;Spencer J Sherwin

  • Hidden physics models: Machine learning of nonlinear partial differential equations

    Maziar Raissi;George Em Karniadakis

  • Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations

    Maziar Raissi;Paris Perdikaris;George Em Karniadakis

  • Physics-informed neural networks for high-speed flows

    Zhiping Mao;Ameya D. Jagtap;George Em Karniadakis

  • NSFnets (Navier-Stokes flow nets): Physics-informed neural networks for the incompressible Navier-Stokes equations

    Xiaowei Jin;Shengze Cai;Hui Li;George Em Karniadakis

  • Discontinuous Galerkin Methods: Theory, Computation and Applications

    Bernardo Cockburn;George E. Karniadakis;Chi-Wang Shu

  • Physics-informed neural networks for inverse problems in nano-optics and metamaterials.

    Yuyao Chen;Lu Lu;George Em Karniadakis;Luca Dal Negro

  • Modeling Uncertainty in Steady State Diffusion Problems via Generalized Polynomial Chaos

    Dongbin Xiu;George Em Karniadakis

  • An adaptive multi-element generalized polynomial chaos method for stochastic differential equations

    Xiaoliang Wan;George Em Karniadakis

  • Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators

    Lu Lu;Pengzhan Jin;Pengzhan Jin;Guofei Pang;Zhongqiang Zhang

Frequent Co-Authors

Paris Perdikaris
Paris Perdikaris University of Pennsylvania
Spencer J. Sherwin
Spencer J. Sherwin Imperial College London
Suchuan Dong
Suchuan Dong Purdue University West Lafayette
Martin R. Maxey
Martin R. Maxey Brown University
Robert M. Kirby
Robert M. Kirby University of Utah
Dongbin Xiu
Dongbin Xiu The Ohio State University
Guang Lin
Guang Lin Purdue University West Lafayette

If you think any of the details on this page are incorrect, let us know.

Report an issue

We appreciate your kind effort to assist us to improve this page, it would be helpful providing us with as much detail as possible in the text box below:

Related Online Degrees & Career Pathways

For students pursuing Mathematics in the USA, exploring related online degrees can open diverse career opportunities. Programs like data analysis programs complement a math background by enhancing skills in managing and interpreting large datasets, a highly sought-after ability in many industries.

Beyond technical fields, many graduates consider advancing their careers with an MBA. If accessibility is a priority, looking into mba programs easy to get into can provide a smoother entry into business leadership roles without excessive competition or stringent admission demands.

For those who prefer flexibility, easiest mba online options allow students to balance work and study, making it easier to gain managerial skills alongside technical expertise.

Finally, for professionals seeking executive-level credentials quickly, the best 1 year dba program online offers a fast-track option to further cement leadership in data-driven business environments.

Best Scientists Citing George Em Karniadakis

Trending Scientists

Recently Published Articles